The asymptotic symmetries in Brans-Dicke theory are analyzed using Penrose's conformal completion method, which is independent of the coordinate system used. These symmetries indeed include supertranslations and Lorentz transformations for an asymptotically flat spacetime. With the Wald-Zoupas formalism, "conserved charges" and fluxes of the Bondi-Metzner-Sachs algebra are computed. The scalar degree of freedom contributes only to the Lorentz boost charge, although it plays a role in various fluxes. The flux-balance laws are further used to constrain displacement memory, spin memory and center-of-mass memory effects.
This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs group. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations bet…
The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS$_4$ generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS$_4$ Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evo…
We study asymptotically flat spacetimes in five spacetime dimensions by Hamiltonian methods, focusing on spatial infinity and keeping all asymptotically relevant nonlinearities in the transformation laws and in the charge-generators. Precise boundary conditions that lead to a consistent variational principle are given. We show that the algebra of asymptotic symmetries, which had not been uncovered before, is a nonlinear deformation of the semi-direct product of the Lorentz algebra by an abelian algebra involving four independent (and not just one) arbitrary functions of the angles on the $3$-s…
We exhibit a Hamiltonian formulation, both for electromagnetism and gravitation, in which it is not required that the Bondi "news" vanish, but only that the incoming news be equal to the outgoing ones. This requirement is implemented by defining the fields on a two-sheeted hyperbolic surface, which we term "the hourglass". It is a spacelike deformation of the complete lightcone. On it one approaches asymptotically (null) past and future infinity while remaining at a fixed (hyperbolic) time, by going to large spatial distances on its two sheets. The Hamiltonian formulation and -- in particular …
The relation between gravitational memory effects and Bondi-Metzner-Sachs symmetry of the asymptotically flat spacetimes is studied in the scalar-tensor theory. For this purpose, the solutions to the equations of motion near the future null infinity are obtained in the generalized Bondi-Sachs coordinates with a suitable determinant condition. It turns out that the Bondi-Metzner-Sachs group is also a semi-direct product of an infinitesimal dimensional supertranslation group and the Lorentz group as in general relativity. There are also degenerate vacua in both the tensor and the scalar sectors …
Super-BMS$_4$ algebras -- also called BMS$_4$ superalgebras -- are graded extensions of the BMS$_4$ algebra. They can be of two different types: they can contain either a finite number or an infinite number of fermionic generators. We show in this letter that, with suitable boundary conditions on the graviton and gravitino fields at spatial infinity, supergravity on asymptotically flat spaces possesses as superalgebra of asymptotic symmetries a (nonlinear) super-BMS$_4$ algebra containing an infinite number of fermionic generators, which we denote SBMS$_4$. These boundary conditions are not on…
Dray and Streubel proposed a definition of angular momentum in general relativity based on `Bondi-Metzner-Sachs (BMS) charges'. I show here that the natural definition of center of mass in this program has an infinite-dimensional ambiguity. (This seems not to have been noticed before because previous work has tacitly carried over a special-relativistic assumption.) A related point is that the natural definition of spin in this context is translation-, but not supertranslation-, invariant.
In this work the asymptotic structure of space-time and the main properties of the Bondi-Metzner-Sachs (BMS) group, which is the asymptotic symmetry group of asymptotically flat space-times, are analysed. Every chapter, except the fourth, begins with a brief summary of the topics that will be dealt through it and an introduction to the main concepts. The work can be divided into three principal parts. The first part includes the first two chapters and is devoted to the development of the mathematical tools that will be used throughout all of the work. In particular we will introduce the notion…
The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poinca…
We use the formalism developed by Wald and Zoupas to derive explicit covariant expressions for the charges and fluxes associated with the Bondi-Metzner-Sachs symmetries at null infinity in asymptotically flat spacetimes in vacuum general relativity. Our expressions hold in non-stationary regions of null infinity, are local and covariant, conformally-invariant, and are independent of the choice of foliation of null infinity and of the chosen extension of the symmetries away from null infinity. While similar expressions have appeared previously in the literature in Bondi-Sachs coordinates (to wh…
We show that the asymptotic infinite dimensional enlarged gauge symmetries constructed for QED are anomalous in Dirac and Weyl semimetals. This symmetry is particularly important in particle physics for its analogy with the Bondi-Metzner-Sachs (BMS) symmetries in gravity, as well as for its connection with QED soft IR theorems. This leads to observable effects, because of the induction of a new current in the material, which carries a memory of the BMS symmetry precursor.
These notes are an introduction to asymptotic symmetries in gauge theories, with a focus on general relativity in four dimensions. We explain how to impose consistent sets of boundary conditions in the gauge fixing approach and how to derive the asymptotic symmetry parameters. The different procedures to obtain the associated charges are presented. As an illustration of these general concepts, the examples of four-dimensional general relativity in asymptotically (locally) (A)dS$_4$ and asymptotically flat spacetimes are covered. This enables us to discuss the different extensions of the Bondi-…
This article reviews one of the most intriguing properties of black hole spacetimes known in the literature -- gravitational memory effect, and its connection with asymptotic symmetries, also termed as Bondi-van der Burg-Metzner-Sachs (BMS) symmetries, emerging near the horizon of black holes. Gravitational memory is a non-oscillatory part of the gravitational wave amplitude which generates a permanent displacement for freely falling test particles or test detectors. We highlight a model scenario where asymptotic symmetries appear as a soldering freedom in the context of stitching of two black…
There exist gravitational memory effects in Brans-Dicke theory. They are closely related to the Bondi-Metzner-Sachs symmetries living on the null infinity in an isolated system. By studying the asymptotically flat spacetime in Brans-Dicke theory and the asymptotic symmetries, one discovers that the displacement memory effect in the tensor sector is due to the vacuum transition caused by the null energy fluxes panetrating the null infinity, while in the scalar sector, the vacuum transition is due to the angular momentum fluxes. Together with the spin and the center-of-mass memory effects, the d…
We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity and satisfy an additional set of conditions which we lay out explicitly. Combined with earlier results on the matching of supertranslation charges, this shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacet…
Recently symmetries of gravity and gauge fields in the asymptotic regions of spacetime have been shown to play vital role in their low energy scattering phenomena. Further, for the black hole spacetime, near horizon symmetry has been observed to play possible role in understanding the underlying degrees of freedom for thermodynamic behaviour of horizon. Following the similar idea, in this paper, we analyzed the symmetry and associated algebra near a timelike surface which is situated at any arbitrary radial position and is embedded in black hole spacetime. In this paper we considered both Schw…
We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side. At null infinity, we find the YM origin of the sub…
We study horizon shells and soldering freedom for extreme black holes and how supertranslation-like Bondi-Metzner-Sachs (BMS) symmetries appear as soldering transformations. Further, for a null shell placed infinitesimally close to the horizon of an extreme Reissner-Nordstr$\ddot{o}$m (RN) black hole, we show superrotation-like symmetries also arise as soldering freedom. Next, considering the interaction of impulsive gravitational waves supported at the horizon shell with test particles, we study how the "memory" (or the imprints) of BMS-like symmetries gets encoded in the geodesics (test part…
Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we…
In this work, conserved charges and fluxes at the future null infinity are determined in the asymptotically flat spacetime for Chern-Simons modified gravity. The flux-balance laws are used to constrain the memory effects. For tensor memories, the Penrose's conformal completion method is used to analyze the asymptotic structures and asymptotic symmetries, and then, conserved charges for the Bondi-Metzner-Sachs algebra are constructed with the Wald-Zoupas formalism. These charges take very similar forms to those in Brans-Dicke theory. For the scalar memory, Chern-Simons modified gravity is rewri…
The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry group of radiating asymptotically flat spacetimes. It has recently received renewed interest in the context of the flat holography and the infrared structure of gravity. In this thesis, we investigate the consequences of considering extensions of the BMS group in four dimensions with superrotations. In particular, we apply the covariant phase space methods on a class of first order gauge theories that includes the Cartan formulation of general relativity and specify this analysis to gravity in asymptotically flat space…
Consider compact objects --such as neutron star or black hole binaries-- in \emph{full, non-linear} general relativity. In the case with zero cosmological constant $Λ$, the gravitational radiation emitted by such systems is described by the well established, 50+ year old framework due to Bondi, Sachs, Penrose and others. However, so far we do not have a satisfactory extension of this framework to include a \emph{positive} cosmological constant --or, more generally, the dark energy responsible for the accelerated expansion of the universe. In particular, we do not yet have an adequate gauge inv…
We consider a recently proposed extension of the Bondi-Metzner-Sachs algebra to include arbitrary infinitesimal diffeomorphisms on a (2)-sphere. To realize this extended algebra as asymptotic symmetries, we work with an extended class of spacetimes in which the unphysical metric at null infinity is not universal. We show that the symplectic current evaluated on these extended symmetries is divergent in the limit to null infinity. We also show that this divergence cannot be removed by a local and covariant redefinition of the symplectic current. This suggests that such an extended symmetry alge…
We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Fina…
Scalaron Quasinormal and Quasi-Bound Modes of Schwarzschild Black Holes in the Bondi-Sachs Formulation of Metric $f(R)$ Gravity
University of Cape Town（开普敦大学）；Botswana International University of Science and Technology（博茨瓦纳国际科学与技术大学）；University of South Africa（南非大学）；University of Oslo（奥斯陆大学）
We study the Newman--Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this topology. To obtain a manifold structure we consider a finer Whitney-type topology. This turns the unit component of the NU group into an infinite-dimensional Lie group. We then study the Lie theoretic properties of this group. Surprisingly, the group operations of the full NU group become discontinuous, whence the NU group does not support a Lie group structure. The NU group c…
In a companion paper we showed that the symmetry group $\mathfrak{G}$ of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group $\mathfrak{G}$ at $\mathcal{I}^{+}$. For each infinitesimal generator of $\mathfrak{G}$, we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries $\mathcal{N}$. However, $\mathcal{N}$ is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of $\mathfrak{G}$ are free of physicall…
In this paper, new exact solutions for locally rotational symmetric (LRS) space-times are obtained within the modified Brans-Dicke theory (MBDT) (Rasouli et al 2014 Class. Quantum Grav. 31 115002). Specifically, extended five-dimensional (5D) versions of Kantowski-Sachs, LRS Bianchi type I and Bianchi type III are investigated in the context of the standard Brans-Dicke theory. We subsequently extract their corresponding dynamics on a 4D hypersurface. Our results are discussed regarding others obtained in the standard Brans-Dicke theory, induced-matter theory and general relativity. Moreover, w…
The expansion history of the Universe reconstructed from a combination of recent data indicates a preference for a changing Dark Energy (DE) density. Moreover, the DE density appears to be increasing with cosmic time, with its equation of state being below -1 on average, and possibly crossing the so-called phantom divide. Scalar-tensor theories, in which the scalar field mediates a force between matter particles, offer a natural framework in which the effective DE equation of state can be less than -1 and cross the phantom barrier. We consider the generalized Brans-Dicke (GBD) class of scalar-…
